Conway's potential function via the Gassner representation

Abstract

We show how Conway's multivariable potential function can be constructed using braids and the reduced Gassner representation. The resulting formula is a multivariable generalization of a construction, due to Kassel-Turaev, of the Alexander-Conway polynomial in terms of the Burau representation. Apart from providing a new efficient method of computing the potential function, our result also removes the sign ambiguity in the current formulas which relate the multivariable Alexander polynomial to the reduced Gassner representation. We also relate the distinct definitions of this representation which have appeared in the literature.